Tag: rotational motion of a rigid body and moment of inertia

Questions Related to rotational motion of a rigid body and moment of inertia

The angular momentum of an electron revolving in a circular orbit is J, What is its magnetic moment? 

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $\frac{mJ}{2e}$

  2. $\frac{eJ}{2m}$

  3. $\frac{2m}{eJ}$

  4. $\frac{emJ}{2}$

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Correct Option: B
Explanation:

According to Bohr modal of hydrogen like atoms, negatively charged electrons revolves around the positively charged nucleus. This uniform circular motion of electrons is equivalent to a current loop which possesses a magnetic dipole moment =IA

I:- current in the loop

A:-area

Consider an electron revolving anticlockwise around a nucleus in an orbit of radius r with speed v and time period T.

Equivalent current,

I= charge/time

=e/t = e/2πr/v

=ev/2πr

Area of current loop ,A=πr2

So , orbital magnetic moment of electron is=IA

=(ev/2πr). πr2

=evr/2

As J is angular momentum. J=mvr

m- mass of electron

So orbital magnetic moment = eJ/2m

$E _n$ and $J _n$ denote the total energy magnitude and the  angular momentum of an electron in the nth allowed orbit of the Both atom .Then:

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $E _n \pi J _n$

  2. $E _n \pi \frac {1} {J}$

  3. $E _n \pi { J } _{ n }^{ 2 }$

  4. $E _n \pi \frac {1} {J^2}$

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Correct Option: C

A wooden block of mass $2\ m$ is hung with the help of a light string of length $l$ in the vertical plane.
A bullet of mass $\dfrac{m}{4}$ moving horizontally with velocity $v _{0}\left(v _{0}=\sqrt{5gl}\right)$ penetrates the block and comes out with velocity $\dfrac{v _{0}}{2}$. The maximum height reached by the block is (Assume string remains vertical till bulled passes through the block)

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $\dfrac{{v} _{0}^{2}}{256\ g}$

  2. $\dfrac{{v} _{0}^{2}}{128\ g}$

  3. $\dfrac{{v} _{0}^{2}}{512\ g}$

  4. $\dfrac{{v} _{0}^{2}}{32\ g}$

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Correct Option: B

A person standing on a rotating platform has his hands lowered. He suddenly outstretch his arms. The angular momentum.

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. Becomes Zero

  2. Increases

  3. Decreases

  4. Remains the same

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Correct Option: B

If a person sitting on a rotating stool with his hands outstretched, suddenly lowers his hands, then his :

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. Kinetic energy will decrease.

  2. Moment of inertia will decrease.

  3. Angular momentum will increase.

  4. Angular velocity will remain constant.

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Correct Option: B
Explanation:

According to conservation of Angular Momentum,
$I \omega$ = constant
Hence, when a person sitting on a rotating stool suddenly  lowers his hands, then his angular velocity will increase and moment of inertia will decrease. 

A man spinning in free space changes the shape of his body, eg. by spreading his arms or curling up. By doing this, he can change his :

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. moment of inertia

  2. angular momentum

  3. angular velocity

  4. rotational kinetic energy

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Correct Option: A,C,D
Explanation:

The moment of inertia can be increased or angular velocity can be decreased by stretching hands outside. Also, smaller the moment of inertia means less resistance to rotation (some rapid corrections have to made to achieve rotational equilibrium), hence change in moment of inertia leads the change in rotational kinetic energy. While angular momentum remains conserved.

Two particles are initially moving with angular momentum $\vec{L _{1}}$ and $\vec{L _{2}}$ in a region of space with no external torque. A constant external torque $\vec{\tau}$ then acts on one particle, but not on the other particle, for a time interval $\Delta{t}$. What is the change in the total angular momentum of the two particles?

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $\vec\Delta L=\vec {L _{1}}-\vec{L _{2}}$

  2. $\Delta L=\dfrac{1}{2}(\vec {L _{1}}-\vec{L _{2}})$

  3. $\vec\Delta L=\tau \Delta t$

  4. $\vec\Delta L$ is not applicable for this system.

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Correct Option: C

uniform disc of mass M and radius R is rotating about its centre of mass (the centre of mass is at rest )with an angular speed $\omega $.the angular momentum of disc about a point A (as shown)will be.

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $M{R^2}\omega + MhR\omega $

  2. $\frac{1}{2}M{R^2}\omega $

  3. $\frac{1}{2}M{R^2}\omega + MhR\omega $

  4. $\frac{1}{2}M{R^2}\omega + 1/2MhR\omega $

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Correct Option: A

when a mass is rotating in a plane about a fixed point, its angular momentum is directed along

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. radius

  2. the tangent to the orbit

  3. a line perpendicular to the plane of rotation

  4. none of above

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Correct Option: C

The angular momentum of a system of particles is conserved 

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. When no external force acts upon the system

  2. When no external torque acts upon the system

  3. When no external impulse acts upon the system

  4. none of these 

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Correct Option: B